Continuous-time Markov chains (CTMCs) are popular modeling formalism that constitutes the underlying semantics for real-time probabilistic systems such as queuing networks, stochastic process algebras, and calculi for systems biology. Prism and Storm are popular model checking tools that provide a number of powerful analysis techniques for CTMCs. These tools accept models expressed as the parallel composition of a number of modules interacting with each other. The outcome of the analysis is strongly dependent on the parameter values used in the model which govern the timing and probability of events of the resulting CTMC. However, for some applications, parameter values have to be empirically estimated from partially-observable executions. In this work, we address the problem of estimating parameter values of CTMCs expressed as Prism models from a number of partially-observable executions. We introduce the class parametric CTMCs -- CTMCs where transition rates are polynomial functions over a set of parameters -- as an abstraction of CTMCs covering a large class of Prism models. Then, building on a theory of algorithms known by the initials MM, for minorization-maximization, we present iterative maximum likelihood estimation algorithms for parametric CTMCs covering two learning scenarios: when both state-labels and dwell times are observable, or just state-labels are. We conclude by illustrating the use of our technique in a simple but non-trivial case study: the analysis of the spread of COVID-19 in presence of lockdown countermeasures.

Latent variable models such as the Variational Auto-Encoder (VAE) have become a go-to tool for analyzing biological data, especially in the field of single-cell genomics. One remaining challenge is the interpretability of latent variables as biological processes that define a cell's identity. Outside of biological applications, this problem is commonly referred to as learning disentangled representations. Although several disentanglement-promoting variants of the VAE were introduced, and applied to single-cell genomics data, this task has been shown to be infeasible from independent and identically distributed measurements, without additional structure. Instead, recent methods propose to leverage non-stationary data, as well as the sparse mechanism shift assumption in order to learn disentangled representations with a causal semantic. Here, we extend the application of these methodological advances to the analysis of single-cell genomics data with genetic or chemical perturbations. More precisely, we propose a deep generative model of single-cell gene expression data for which each perturbation is treated as a stochastic intervention targeting an unknown, but sparse, subset of latent variables. We benchmark these methods on simulated single-cell data to evaluate their performance at latent units recovery, causal target identification and out-of-domain generalization. Finally, we apply those approaches to two real-world large-scale gene perturbation data sets and find that models that exploit the sparse mechanism shift hypothesis surpass contemporary methods on a transfer learning task. We implement our new model and benchmarks using the scvi-tools library, and release it as open-source software at https://github.com/Genentech/sVAE.

Personalized prediction of responses for individual entities caused by external drivers is vital across many disciplines. Recent machine learning (ML) advances have led to new state-of-the-art response prediction models. Models built at a population level often lead to sub-optimal performance in many personalized prediction settings due to heterogeneity in data across entities (tasks). In personalized prediction, the goal is to incorporate inherent characteristics of different entities to improve prediction performance. In this survey, we focus on the recent developments in the ML community for such entity-aware modeling approaches. ML algorithms often modulate the network using these entity characteristics when they are readily available. However, these entity characteristics are not readily available in many real-world scenarios, and different ML methods have been proposed to infer these characteristics from the data. In this survey, we have organized the current literature on entity-aware modeling based on the availability of these characteristics as well as the amount of training data. We highlight how recent innovations in other disciplines, such as uncertainty quantification, fairness, and knowledge-guided machine learning, can improve entity-aware modeling.

Implicit processes (IPs) are a generalization of Gaussian processes (GPs). IPs may lack a closed-form expression but are easy to sample from. Examples include, among others, Bayesian neural networks or neural samplers. IPs can be used as priors over functions, resulting in flexible models with well-calibrated prediction uncertainty estimates. Methods based on IPs usually carry out function-space approximate inference, which overcomes some of the difficulties of parameterspace approximate inference. Nevertheless, the approximations employed often limit the expressiveness of the final model, resulting, e.g., in a Gaussian predictive distribution, which can be restrictive. We propose here a multi-layer generalization of IPs called the Deep Variational Implicit process (DVIP). This generalization is similar to that of deep GPs over GPs, but it is more flexible due to the use of IPs as the prior distribution over the latent functions. We describe a scalable variational inference algorithm for training DVIP and show that it outperforms previous IPbased methods and also deep GPs. We support these claims via extensive regression and classification experiments. We also evaluate DVIP on large datasets with up to several million data instances to illustrate its good scalability and performance. The Bayesian approach has become popular for capturing the uncertainty associated to the predictions made by models that otherwise provide point-wise estimates, such as neural networks (NNs) (Gelman et al., 2013; Gal, 2016; Murphy, 2012). However, when carrying out Bayesian inference, obtaining the posterior distribution in the space of parameters can become a limiting factor since it is often intractable. Symmetries and strong dependencies between parameters make the approximate inference problem much more complex. This is precisely the case in large deep NNs. Nevertheless, all these issues can be alleviated by carrying out approximate inference in the space of functions, which presents certain advantages due to the simplified problem.

The symbolic AI community is increasingly trying to embrace machine learning in neuro-symbolic architectures, yet is still struggling due to cultural barriers. To break the barrier, this rather opinionated personal memo attempts to explain and rectify the conventions in Statistics, Machine Learning, and Deep Learning from the viewpoint of outsiders. It provides a step-by-step protocol for designing a machine learning system that satisfies a minimum theoretical guarantee necessary for being taken seriously by the symbolic AI community, i.e., it discusses "in what condition we can stop worrying and accept statistical machine learning." Unlike most textbooks which are written for students trying to specialize in Stat/ML/DL and willing to accept jargons, this memo is written for experienced symbolic researchers that hear a lot of buzz but are still uncertain and skeptical. Information on Stat/ML/DL is currently too scattered or too noisy to invest in. This memo prioritizes compactness, citations to old papers (many in early 20th century), and concepts that resonate well with symbolic paradigms in order to offer time savings. It prioritizes general mathematical modeling and does not discuss any specific function approximator, such as neural networks (NNs), SVMs, decision trees, etc. Finally, it is open to corrections. Consider this memo as something similar to a blog post taking the form of a paper on Arxiv.

One reason deep learning exploded over the last decade was the availability of programming languages that could automate the math -- college-level calculus -- that is needed to train each new model. Neural networks are trained by tuning their parameters to try to maximize a score that can be rapidly calculated for training data. The equations used to adjust the parameters in each tuning step used to be derived painstakingly by hand. Deep learning platforms use a method called automatic differentiation to calculate the adjustments automatically. This allowed researchers to rapidly explore a huge space of models, and find the ones that really worked, without needing to know the underlying math.

Identifying predictive factors via multivariable statistical analysis is for rare diseases often impossible because the data sets available are too small. Combining data from different medical centers into a single (larger) database would alleviate this problem, but is in practice challenging due to regulatory and logistic problems. Federated Learning (FL) is a machine learning approach that aims to construct from local inferences in separate data centers what would have been inferred had the data sets been merged. It seeks to harvest the statistical power of larger data sets without actually creating them. The FL strategy is not always feasible for small data sets. Therefore, in this paper we refine and implement an alternative Bayesian Federated Inference (BFI) framework for multi center data with the same aim as FL. The BFI framework is designed to cope with small data sets by inferring locally not only the optimal parameter values, but also additional features of the posterior parameter distribution, capturing information beyond that is used in FL. BFI has the additional benefit that a single inference cycle across the centers is sufficient, whereas FL needs multiple cycles. We quantify the performance of the proposed methodology on simulated and real life data.

An evident challenge ahead for the integrated circuit (IC) industry in the nanometer regime is the investigation and development of methods that can reduce the design complexity ensuing from growing process variations and curtail the turnaround time of chip manufacturing. Conventional methodologies employed for such tasks are largely manual; thus, time-consuming and resource-intensive. In contrast, the unique learning strategies of artificial intelligence (AI) provide numerous exciting automated approaches for handling complex and data-intensive tasks in very-large-scale integration (VLSI) design and testing. Employing AI and machine learning (ML) algorithms in VLSI design and manufacturing reduces the time and effort for understanding and processing the data within and across different abstraction levels via automated learning algorithms. It, in turn, improves the IC yield and reduces the manufacturing turnaround time. This paper thoroughly reviews the AI/ML automated approaches introduced in the past towards VLSI design and manufacturing. Moreover, we discuss the scope of AI/ML applications in the future at various abstraction levels to revolutionize the field of VLSI design, aiming for high-speed, highly intelligent, and efficient implementations.

Numerous applications of machine learning involve representing probability distributions over high-dimensional data. We propose autoregressive quantile flows, a flexible class of normalizing flow models trained using a novel objective based on proper scoring rules. Our objective does not require calculating computationally expensive determinants of Jacobians during training and supports new types of neural architectures, such as neural autoregressive flows from which it is easy to sample. We leverage these models in quantile flow regression, an approach that parameterizes predictive conditional distributions with flows, resulting in improved probabilistic predictions on tasks such as time series forecasting and object detection. Our novel objective functions and neural flow parameterizations also yield improvements on popular generation and density estimation tasks, and represent a step beyond maximum likelihood learning of flows. Reasoning about uncertainty via the language of probability is important in many application domains of machine learning, including medicine (Saria, 2018), robotics (Chua et al., 2018; Buckman et al., 2018), and operations research (Van Roy et al., 1997). Especially important is the estimation of predictive uncertainties (e.g., confidence intervals around forecasts) in tasks such as clinical diagnosis (Jiang et al., 2012) or decision support systems (Werling et al., 2015; Kuleshov and Liang, 2015). Normalizing flows (Rezende and Mohamed, 2016; Papamakarios et al., 2019; Kingma et al., 2016) are a popular framework for defining probabilistic models, and can be used for density estimation (Papamakarios et al., 2017), out-of-distribution detection (Nalisnick et al., 2019), content generation (Kingma and Dhariwal, 2018), and more. Flows feature tractable posterior inference and maximum likelihood estimation; however, maximum likelihood estimation of flows requires carefully designing a family of bijective functions that are simultaneously expressive and whose Jacobian has a tractable determinant.

We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off between a high probability of convergence and a high convergence speed. Even in the limit case, where convergence is guaranteed, our learned optimization algorithms provably outperform related algorithms based on a (deterministic) worst-case analysis. Our results rely on PAC-Bayes bounds for general, unbounded loss-functions based on exponential families. By generalizing existing ideas, we reformulate the learning procedure into a one-dimensional minimization problem and study the possibility to find a global minimum, which enables the algorithmic realization of the learning procedure. As a proof-of-concept, we learn hyperparameters of standard optimization algorithms to empirically underline our theory.